A respiratory activity signal is a signal measuring the variation of a quantity related to the respiratory activity of the patient, such as the air flow rate and pressure or the oxygen and carbon dioxide concentration at the entry of his/her respiratory tracts or the oxygen concentration in the blood. These quantities may be measured with non-invasive measuring apparatuses, for example a flow rate or pressure sensor integrated to a mask placed in front of the mouth of the patient or an oxymeter, or with internal sensors, for example pressure sensors, placed in the respiratory circuit of the patient. Such signals may also be inferred from electrocardiogram signals.
Respiratory activity consists of a succession of respiratory cycles, comprising an inhalation phase and exhalation phase, at a frequency called a respiratory frequency. Therefore, the respiratory activity signals are quasi-periodic signals, comprising a succession of elementary signals, each of these elementary signals being characteristic of a respiratory cycle.
The analysis of these signals allows detection of respiratory disorders or abnormalities such as sleep apnea or asthma. However, this analysis is generally limited to the determination of the respiratory frequency and of its variability, and of the amplitude of these signals, and no analysis of the waveform of these signals is carried out.
Now, the waveform of respiratory activity signals is characteristic of this respiratory activity and their analysis may allow efficient detection of possible respiratory abnormalities.
Many methods for analyzing and characterizing a periodic signal are known. In particular, frequency analysis of a signal allows a description of this signal in Fourier space. Fourier decomposition actually consists in breaking down a periodic signal of frequency f into an infinite sum of sinusoidal functions with frequencies which are multiples of f, weighted with Fourier coefficients. These Fourier coefficients, which form a coding of the analyzed signal, are characteristic parameters of this signal. In practice, the number of retained Fourier coefficients is limited and only the first terms of the Fourier decomposition are kept. These terms however have to be in sufficient number in order to characterize the signal efficiently.
Now, respiratory activity signals are anharmonic signals, i.e. non-linear signals, and the Fourier decomposition of such signals requires that a large number of coefficients be retained, coefficients to which it is difficult to give a physical meaning. Fourier decomposition is therefore unsuitable for analyzing these signals.